Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42×C5 · Schur multiplier (H2) = C4 |
| direct product | C3×C4×C5×Dic5 |
| derived | C5 ⋊ C3×C42×C5 |
| Hall | C3×C52 ⋊ C42 |
| Sylow | C52 ⋊ C3×C42 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
480 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 392);